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Benefits of Hypergraphs for Density-Based Clustering

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Názov: Benefits of Hypergraphs for Density-Based Clustering
Autori: Hauseux, Louis, Avrachenkov, Konstantin, Zerubia, Josiane
Prispievatelia: Hauseux, Louis
Zdroj: 2024 32nd European Signal Processing Conference (EUSIPCO). :2302-2306
Informácie o vydavateľovi: IEEE, 2024.
Rok vydania: 2024
Predmety: percolation, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], hypergraphs, [INFO.INFO-TS] Computer Science [cs]/Signal and Image Processing, geometric graphs, density estimator, [INFO] Computer Science [cs], hierarchical clustering
Popis: Many of clustering algorithms are based on density estimates in R^d . Building geometric graphs on the dataset X is an elegant way of doing this. In fact, the connected components of a geometric graph match exactly with the high-density clusters of the 1-Nearest Neighbor density estimator. In this paper, We show that the natural way to generalize geometric graphs is to use hypergraphs with a more restrictive notion of connected component called K-Polyhedron. Herein, we prove that K-polyhedra correspond to high-density clusters of K-Nearest Neighbors density estimator. Furthermore, the percolation phenomenon is omnipresent behind the family of clustering algorithms we look at in this paper.
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DOI: 10.23919/eusipco63174.2024.10715271
Rights: STM Policy #29
CC BY NC
Prístupové číslo: edsair.doi.dedup.....d9e2fa01c6bdfe6057e5a7b9d402b5cb
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  Data: Benefits of Hypergraphs for Density-Based Clustering
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  Data: Hauseux, Louis
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  Data: <i>2024 32nd European Signal Processing Conference (EUSIPCO)</i>. :2302-2306
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  Data: IEEE, 2024.
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  Data: Many of clustering algorithms are based on density estimates in R^d . Building geometric graphs on the dataset X is an elegant way of doing this. In fact, the connected components of a geometric graph match exactly with the high-density clusters of the 1-Nearest Neighbor density estimator. In this paper, We show that the natural way to generalize geometric graphs is to use hypergraphs with a more restrictive notion of connected component called K-Polyhedron. Herein, we prove that K-polyhedra correspond to high-density clusters of K-Nearest Neighbors density estimator. Furthermore, the percolation phenomenon is omnipresent behind the family of clustering algorithms we look at in this paper.
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      – TitleFull: Benefits of Hypergraphs for Density-Based Clustering
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              Y: 2024
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